Question

Write an equation of the line that passes through the point

(6,-5) and is parallel to the line whose equation is 2x - 3y = 11

Answer 1

First we have to transform 2x-3y=11 into common form y=ax+b, so
2x-3y=11 /-2x both side
-3y=11-2x /:(-3) both side
y=
`(2)/(3)x- (11)/(3)`
Parallel condition is
`a_(1) = a_(2)`
Our
`a_(1)= (2)/(3)`, so we are sure that new equation looks
y=
`(2)/(3)x+b`
To find b, we can substitute x and y from point (6,-5).
-5=
`(2)/(3)*6+b`
-5=4+b /-4 both side
-9=b
So, the result is
y=
`(2)/(3)-9`